Correlation between bound and continuous states of three identical particles

Nicolas Douguet, Juan Blandón, Viatcheslav Kokoouline

We discuss collision of three identical particles and derive scattering selection rules from initial to final states of the particles. We use either hyperspherical or Jacobian coordinates depending on which one is best suited to describe three different configurations of the particles: (1) three free particles, (2) a quasi-bound trimer or (3) a dimer and a free particle. We summarize quantum numbers conserved during the collision as well as quantum numbers that are appropriate for a given configuration but may change during the scattering process. The total symmetry of the system depends on these quantum numbers. Based on the selection rules, we construct correlation diagrams between different configurations before and after a collision. In particular, we describe a possible fragmentation of the system into one free particle and a dimer, which can be used, for example, to identify possible decay products of quasi-stationary three-body states or three-body recombination.

A. K. Chaudhuri

A. K. Chaudhuri

Fabrizio Buscemi, Paolo Bordone

We describe an efficient theoretical criterion suitable for the evaluation of the tripartite entanglement of any mixed three-boson or three-fermion state, based on the notion of the entanglement of particles for bipartite systems of identical particles. Our approach allows one to quantify the accessible number of quantum correlations in the systems without any violation of the local particle number superselection rule. A generalization of the tripartite negativity is here applied to some correlated systems including the continuous-time quantum walks of identical particles (for both bosons and fermions) and compared with other criteria recently proposed in the literature. Our results show the dependence of the entanglement dynamics upon the quantum statistics: The bosonic bunching results in a low number of quantum correlations while Fermi-Dirac statistics allows for higher values of the entanglement.

Francesco Calogero, Carlo Marchioro

Lower bounds to the ground-state energy of a system composed of N identical particles interacting by two-body forces (and possibly also with an external potential) are derived. They are expressed in terms of the ground-state energies of (simpler) systems composed of a smaller number of particles having masses and/or interactions different from the original ones. This reduction process may be continued all the way down to systems involving one and two particles only. The generalization to systems containing some identical and some distinguishable particles is also discussed.

J. H. Macek